Variance Estimation

PROC SURVEYREG uses the Taylor series method or replication (resampling) methods to estimate sampling errors of estimators
based on complex sample designs (Fuller, 2009; Woodruff, 1971; Fuller, 1975; Fuller et al., 1989; Särndal, Swensson, and Wretman, 1992; Wolter, 2007; Rust, 1985; Dippo, Fay, and Morganstein, 1984; Rao and Shao, 1999; Rao, Wu, and Yue, 1992; Rao and Shao, 1996). You can use the VARMETHOD= option to specify a variance estimation method to use. By default, the Taylor series method is used. However, replication
methods have recently gained popularity for estimating variances in complex survey data analysis. One reason for this popularity
is the relative simplicity of replication-based estimates, especially for nonlinear estimators; another is that modern computational
capacity has made replication methods feasible for practical survey analysis.

Replication methods draw multiple replicates (also called subsamples) from a full sample according to a specific resampling
scheme. The most commonly used resampling schemes are the balanced repeated replication (BRR) method and the jackknife method. For each replicate, the original weights are modified for the PSUs in the replicates to create replicate weights.
The parameters of interest are estimated by using the replicate weights for each replicate. Then the variances of parameters
of interest are estimated by the variability among the estimates derived from these replicates. You can use the REPWEIGHTS statement to provide your own replicate weights for variance estimation.

The following sections provide details about how the variance-covariance matrix of the estimated regression coefficients is
estimated for each variance estimation method.